$2.$ Sue Sayer is employed as a forecasting analyst for the Barry M$.$ Stiff Casket Corporation. Ms$.$ Sayer has collected the following sales data on Stiff$$s best$-$selling casket, Model $12-$A:

Period Sales

$125$

$235$

$330$

$437$

$540$

$642$

$738$

$845$

$950$

a$.$ What$$s the four$-$period moving average forecast for period $7$ made at the end of period $6?$

b$.$ If the forecast for period $1$ were $20,$ what would be the forecast for period $2$ made at the end of period $1,$ using basic exponential smoothing and a smoothing constant of $\backslash$alpha $=0\mathrm{.}2?$

c$.$ If the base at the end of period $7$ were $39$ and the trend at the end of period $7$ were $4(\backslash$alpha $=0\mathrm{.}2,\backslash$beta $=0\mathrm{.}4),$ what would be the forecast for period $9$ made at the end of period $8?$

d$.$ Given the model described in c$,$ what would be the forecast for period $11$ made at the end of period $9?$

e$.$ Given the model described in c and d$,$ what would be the forecast for period $12$ made at the end of period $9?$

f$.$ What would be the mean absolute deviation of forecast errors, given that forecasts for periods $6,7,8,$ and $9$ were $40,35,45,$ and $65,$ respectively?